Test for a Difference in Two Odds Ratios

Testing for a statistical difference between two odds ratio estimates can be useful in determining if an association has statistically different effects in different groups or strata of a variable.  For example, maybe an association is stronger for older individuals than younger individuals.  To test for such a difference we need the odds ratio estimate (or more precisely the natural log of the odds ratio estimate, aka the beta estimate from a logistic regression) and the standard error of the log odds ratio.

If you don't have access to the primary data and need to estimate the standard error from a 95% confidence interval (95% CI), see this blog entry.  If you have forgotten how to calculate the standard error of the log odds ratio use this formula:
SE(logOR)=1n1+1n2+1n3+1n4−−−−−−−−−−−−−−−√

To test if two odds ratios are significantly different and get a p-value for the difference follow these steps:
(1) Take the absolute value of the difference between the two log odds ratios. We will call this value δ.
(2) Calculate the standard error for δ, SE(δ), using the formula:
SE21+SE22−−−−−−−−−
√

(3) Calculate the Z score for the test: z=δ/SE(δ)
(4) Calculate the p-value from the z score. The p-value can be easily calculated in R or Microsoft Excel using the below formulas.

R: P-value=2*(1-pnorm(Z))
MS Excel: P-value=2*(1-(NORMDIST(Z,0,1,TRUE)))

Calculate Your Probability of Becoming a Principal Investigator

Ever wonder what your chances are of becoming a principal investigator (PI)?  Well, researchers at the Weizmann Institute just made it a lot easier to predict your odds of successfully becoming a PI.  Machine learning techniques borrowed from gene expression were applied to publication records of PI's to see if there were certain attributes that could predict future success of landing an academic position.  The verdict: success in academia is highly predictable (AUC=0.83)!  It appears that successful PI candidates have both quantity and quality to their publication records.  Important factors for becoming a PI include number of first author publications, journal impact factor, and impact factor of your articles relative to other articles in the journal.  Factors not related to publication record, however, were also important.  These attributes include gender and the rank of their university.  To calculate your likelihood of becoming a principal investigator, follow this link to the PI Predictor.